1. Field of the Invention
This invention relates to electronic oscillators, and more particularly to a circuit and method for a quartz crystal oscillator. Described herein are means for limiting loading effects in a crystal oscillator, thereby improving the crystal resonator quality factor (or Q). This is advantageous, since a higher Q is generally associated with improved frequency stability and lower phase jitter. Such precision oscillators are widely used as timing sources in various digital integrated circuits.
2. Description of the Related Art
Modern high-speed digital systems typically employ clock-based timing circuitry. A clock is commonly used to supply a timing reference to synchronize the state changes in logic devices, such as counters, flip-flops, etc. More complex integrated circuits (ICs), such as microprocessors, typically include clock circuitry internal to the IC for this purpose. A clock circuit is a form of electronic oscillatorxe2x80x94i.e., a circuit that generates a periodic time-varying output. The most important characteristic for an oscillator used in a clock circuit is that the frequency of oscillation be very consistent, both on a long term and a short term basis. If the frequency of an oscillator changes slowly over time, as a result of temperature, aging effects, etc, the oscillator is said to xe2x80x9cdrift.xe2x80x9d In many applications, especially those in which the oscillator is being used for timing purposes, drift is extremely undesirable. For this reason, oscillators are often made to operate within an oven, so that variations in the ambient temperature can be avoided. Short term fluctuations in the operating frequency are usually characterized as xe2x80x9cphase jitter,xe2x80x9d since they may occur within a span of a few cycles and may be modeled as a noise source interfering with an ideal oscillator.
Oscillators depend on the use of regenerative feedback from the output of the oscillator back to its input. In this context, the term xe2x80x9cregenerativexe2x80x9d refers to the fact that the magnitude and phase of the feedback signal are such that it reinforces the input signal, thereby sustaining oscillation. This principle is illustrated in FIG. 1. In the elementary oscillator represented in FIG. 1, an amplifier 50 increases the magnitude of any signal present at its input by a gain factor A. A phase shift network 52 phase-shifts the signal at the output of the amplifier by an angle dependent on the frequency xcfx86(xcfx89) of the signal. A summing junction 54 combines the input signal with the phase-shifted, amplified version of the input signal (i.e., the feedback signal), and couples the composite signal into the amplifier 50.
The phase shift network 52 in any oscillator contains reactive components (i.e., capacitors and/or inductors), to achieve a frequency dependent phase shift. Reactive components are fundamentally different from resistive components, since they can store (but not dissipate) energy. Resistive components, on the other hand, cannot store energy and dissipate electrical energy in the form of heat. Furthermore, the voltage across an inductor or capacitor leads or lags the current through the inductor or capacitor by xcfx80/2 radians (or, equivalently, 90xc2x0), respectively. In contrast, the voltage across a resistor is always in phase with the current. The ratio of voltage across an inductor or capacitor to the current through the inductor or capacitor is known as the inductive or capacitive reactance, respectively. By the same token, the ratio of the voltage to the current in a resistor defines its resistance. In general, for a network containing a combination of resistance and capacitive or inductive reactance, the ratio of voltage to current is known as the impedance.
In a system such as that represented in FIG. 1, oscillation may be induced by an externally applied signal, or by noise, which is always present in an electronic circuit. Noise arising from random physical processes (e.g., thermally-induced molecular motion) is comprised of an entire band of frequencies. A small signal 56 represents one of the frequency components associated with random noise at the input of the summing junction 54. The random signal 56 passes through amplifier 50, emerging at the output 58 with increased amplitude and a different phase angle. Note that the phase relationship between the input signal 56 and the amplified signal 58 is not conducive to sustained oscillation. Whereas the input signal 56 is initially increasing, the amplified version 58 is decreasing. Consequently, if these signals were combined in the summing junction 54, the noise signal 56 would not be reinforced by the feedback signal 58. However, the effect of the phase shift network 52 is to further alter the phase angle of the amplifier output, producing a signal 60 that has the same phase angle as the initial random signal 56. When the in-phase, amplified signal 60 is combined with the input signal 56 in the summing junction 54, it reinforces the input signal. Under these circumstances, the oscillator will generate the signal continuously.
For continuous oscillation to occur, an oscillator must provide a phase shift of 2xcfx80 radians (or, equivalently, 360xc2x0) at the frequency of oscillation. The phase shift is necessary to reinforce the input signal, as described above. As mentioned earlier, the phase angle associated with phase shift network 52 is frequency dependent. Thus, there is just one (fundamental) frequency at which the phase angle of the feedback signal will be 2xcfx80 radians, and the oscillator operates at only this frequency. In practice, the frequency of an oscillator can be made adjustable, by incorporating variable reactive components in the phase shift network. In addition to the necessary phase shift, the oscillator must also have sufficient gain to overcome losses in the resistive components of the oscillator. Without the gain provided by the amplifier, these losses would eventually attenuate the oscillatory signal.
There are a variety of ways to create a oscillator. A classic approach, known as an RC ring oscillator, consists of series-connected phase shift stages, in which the combined phase shift is sufficient to achieve oscillation at the desired operating frequency. For example, an RC ring oscillator can be formed by connecting four stages in series, each stage having a phase shift of xcfx80/2 radians at the desired frequency. By connecting the output of the fourth stage to the input of the first, an overall phase shift of 2xcfx80 radians results. If there is sufficient gain, the RC ring oscillator will sustain oscillation. Although this technique is straightforward, it tends to be noisy and lacks sufficient frequency stability for many applications.
A better approach, the LC oscillator, uses both inductors and capacitors in the phase shift network to obtain the necessary 2xcfx80 radians of phase shift. (xe2x80x9cLCxe2x80x9d oscillators are so named because the traditional symbols for inductance and capacitance are L and C, respectively).
Inductors and capacitors are complementary. Inductive reactance is positive, while capacitive reactance is negative. Moreover, inductive reactance increases in magnitude with frequency, while capacitive reactance decreases. The impedance of a circuit comprising a series combination of an inductor and capacitor is given by:       Z    ⁡          (      ω      )        =            j      ⁢              xe2x80x83            ⁢              ω        ·        L              -          j              ω        ·        C            
where Z is impedance (in ohms), L is inductance (in Henries), C is capacitance (in Farads), and xcfx89 is frequency (in radians per second). Note that Z(xcfx89) becomes zero when xcfx892LC=1.       ω    0    =      1                  L        ·        C            
The frequency xcfx890 at which this occurs is known as the resonant frequency for the given LC pair, and the resonant LC network is referred to as a xe2x80x9ctankxe2x80x9d circuit. Equivalently, the resonant frequency is defined as the frequency at which the inductive and capacitive reactances cancel. A tank circuit operating at its resonant frequency is said to be xe2x80x9cresonatingxe2x80x9d or xe2x80x9cat resonance.xe2x80x9d
At the resonant frequency the impedance of the LC network becomes real (since, at resonance, the inductive and capacitive reactance become equal in magnitude and opposite in sign, and therefore, cancel). An LC oscillator will preferentially oscillate at the resonant frequency of its LC network. When operated at its natural resonant frequency, the frequency stability of a properly designed LC oscillator is inherently better than that of oscillators based on RC phase shift networks.
A quartz crystal is an electromechanical device that behaves like a resonant inductor-capacitor combination in an oscillator. A quartz crystal is often represented by an equivalent circuit consisting of an inductor, a capacitor and a resistor connected in series, as shown in FIG. 2a. As mentioned earlier, the frequency of oscillation in an LCR oscillator is determined by the phase shift due to the reactive components in the LCR networkxe2x80x94i.e., the inductor and capacitor. The network shown to the right in FIG. 2a is commonly referred to as a series LCR (i.e., inductance-capacitance-resistance) circuit. The effective values of the reactive components (i.e., the inductor and capacitor) can be much different in magnitude than is achievable with discrete inductors and capacitors. Therefore, crystals are desirable for use in high-frequency oscillators. For example, a crystal 10 with a 25 MHz resonant frequency is equivalent to an inductance 10a of 2.9 mH, in series with a capacitance 10b of 14 fF and a resistance 10c of 10 xcexa9. In addition, the effective inductance and capacitance of a crystal are quite stable, minimizing variations in the resonant frequency of the crystal over time and with changes in temperature. Because of their stability and their suitability for use at high frequencies, crystals are the preferred resonant component for the oscillators employed in digital systems.
In the equivalent circuit for crystal 10, the inductive reactance LX 10a typically equals the capacitive reactance CX 10b. In other words, at frequencies of interest, the crystal appears series resonant. For practical considerations relating to oscillator design, most crystal oscillators do not operate the crystal at its intrinsic resonant frequency, but instead resonate the crystal in combination with a parallel capacitor.
As stated earlier, reactive components do not dissipate power. Consequently, once oscillation is started in an LC circuit consisting of an ideal inductor and capacitor, it will continue indefinitely. Real components, of course, always contain some resistance (shown as resistor RX 10c in FIG. 2a). Accordingly, a figure of merit known as the xe2x80x9cQxe2x80x9d or xe2x80x9cquality factor,xe2x80x9d is often used to characterize a resonant LCR network (or a crystal). The Q is defined to be the ratio of the energy stored in the LCR network to the energy dissipated, during one cycle at a given frequency. This criterion is roughly equivalent to evaluating how closely the LCR network approximates an ideal LC (i.e., lossless) network. Thus, a crystal with a high Q (e.g., Q greater than 50,000) loses very little energy to intrinsic resistance.
In a practical oscillator, energy must constantly be supplied to compensate for losses in non-ideal components, or oscillation will eventually cease. This energy is supplied by the amplifier within the oscillator. In fact, the amplifier within an oscillator creates a negative resistance, overcoming the losses due to resistance within the non-ideal resonant network. This provides an alternative model to that shown in FIG. 1, which is particularly useful for designing crystal oscillators.
FIG. 2b illustrates a simple oscillator employing a resonant network consisting of crystal X1 10, together with a parallel capacitance CP 12. Also connected in parallel with the crystal is a bias resistor RB 14. A transistor Q1 16 serves as the amplifier for the oscillator, and supplies power dissipated in the resistance of the crystal. A capacitor C1 18 is connected from the gate to the source of transistor Q1 16, and another capacitor C2 20 is connected from the drain to the source. The function of these capacitors is described below.
FIG. 3 contains an equivalent circuit for the oscillator of FIG. 2b. The circuit is divided, with the components on the right representing transistor Q1 16 and capacitors C1 18 and C2 20. The components on the left represent the crystal X1 10 (within the dashed lines), parallel capacitor CP 12, and bias resistor RB 14. This division will be used to analyze the impedance presented by Q1, C1 and C2 to the resonant network (X1, CP and RB) on the left. In the network on the right, VX represents the voltage across the crystal (which is also the gate-to-drain voltage of transistor Q1). V1 and V2 are the voltage across C1 and C2, respectively. Note that V1 is also the gate-to-source voltage of transistor Q1. A loop current I1 enters node 22, and a second loop current I2 enters capacitor C2 20. The drain current ID in transistor Q1 is represented by a voltage dependent current source 16, the magnitude of which is the product of the transconductance of Q1 with the gate-to-source voltage of Q1:
The voltages around the network must add to zero: V2 =VX+V1 
Voltages V1 and V2 are developed by the current I1 through capacitor C1, and I2 through C2, respectively. These relationships may be expressed in the complex frequency domain :       V    1    =                              -                      I            1                                    sC          1                    ⁢              xe2x80x83            ⁢      and      ⁢              xe2x80x83            ⁢              V        2              =                  I        2                    sC        2            
Finally, the current I2 can be defined in terms of I1 and the transistor drain current ID:
I2=I1xe2x88x92ID=I1xe2x88x92gmxc2x7V1
The above equations can be solved for VX in terms of I1 and the fixed component values:       V    x    =            I      1        ·          [                        1                      sC            1                          +                  1                      sC            2                          +                              g            m                                              s              2                        ⁢                          C              1                        ⁢                          C              2                                          ]      
Dividing both sides of the above equation by I1 yields the impedance seen by the resonant network (X1 10, CP 12, and RB 14 in FIG. 3). In the continuous frequency domain, the expression for the impedance is obtained by substituting s=jxcfx89:   Z  =                    V        x                    I        1              =                  1                  j          ⁢                      xe2x80x83                    ⁢                      ωC            1                              +              1                  j          ⁢                      xe2x80x83                    ⁢                      ωC            2                              -                        g          m                                      ω            2                    ⁢                      C            1                    ⁢                      C            2                              
The rightmost term in the above expression is significant. It is a negative real quantity, and therefore, represents a negative resistance. While a conventional resistor dissipates energy, a negative resistor is an energy source. The negative resistance attributed to Q1, together with C1 and C2, sustains oscillation by replacing the energy in the crystal that would otherwise be lost in the non-ideal components of the resonant network. In fact, the circuit represented in FIG. 3 will oscillate as long as:       R    x     less than             g      m                      ω        2            ⁢              C        1            ⁢              C        2            
in other words, as long as the magnitude of the negative resistance is greater than that of the intrinsic resistance of the crystal.
In addition to energy loss, the intrinsic resistance in a crystal degrades its performance in another way. The impedance of a series LCR circuit is frequency dependent, attaining a minimum value at the resonant frequency. FIGS. 4a and 4b contain magnitude and phase plots, respectively, of the impedance of an LCR network (equivalent to a quartz crystal) vs. frequency. The component values for this simulation are:       L    =          0.1      ⁢              xe2x80x83            ⁢      H            C    =          0.01      ⁢              xe2x80x83            ⁢      pF            R    =          5      ⁢              xe2x80x83            ⁢      Ω      
These values of inductance and capacitance result in a resonant frequency of xcfx890=31.623xc3x97106 radians per second (i.e., 5.0329 MHz). In FIG. 4a, note that in the vicinity of the resonant frequency, the impedance of the LCR network drops sharply, resulting in a dip in the voltage across the network. The abruptness of this drop in impedance is related to the Q of the network; the higher the Q1 the more precipitous the drop in impedance. Because of this characteristic, a high Q LCR network is useful in frequency selective circuits, such as filters and oscillators. In particular, increasing the Q of the resonant network in an oscillator generally leads to a more stabile operating frequency.
Recall from the discussion of the oscillator block diagram in FIG. 1 that the feedback signal must have the proper phase angle (i.e., 2xcfx80 radians) for oscillation to occur. In practice, the frequency of oscillation may be perturbed by noise and other random influences. As mentioned earlier, these influences may cause a slow drift away from the nominal operating frequency of the oscillator, or may produce transient deviations, known as phase jitter. However, these phenomena are suppressed by a resonant LC network with a high Q. Refer now to FIG. 4b, showing the phase angle of the impedance of the LCR network. Note that the phase angle has an extremely steep slope in the vicinity of the resonant frequency xcfx890. This implies that a signal at a slightly different frequency xcfx890xc2x1xcex94xcfx89 passing through the network will be subjected to a large phase shift (away from the ideal phase angle of 2xcfx80 radians), thus rendering it incapable of sustained oscillation.
Resistive losses in an LCR network reduce the Q of the network, degrading its frequency selectivity. FIGS. 5a and 5b plot the magnitude and phase of the impedance of an LCR network similar to that in FIGS. 4a and 4b, but with the intrinsic resistance increased from 5xcexa9 to 50xcexa9. Note that the magnitude at resonance does not decrease as much as in the previous case, and the slope of the phase at xcfx890 is also not as sharp. Therefore, the frequency selectivity of the LCR circuit represented in FIGS. 5a and 5b is not as good as that of FIGS. 4a and 4b. 
Unfortunately, the most commonly employed crystal oscillator circuits require the use of bias resistors coupled to the crystal. The crystal is typically treated as an inductance, and resonated with a parallel capacitor (such as CP 12 in FIG. 2b). In this configuration, the intrinsic resistance of the crystal appears transformed as a very high parallel resistance. The presence of the bias resistors reduces this parallel resistance, increasing the energy dissipated and severely degrading the Q of the resonant network.
It would be desirable to have a crystal oscillator circuit that avoids the reduction in Q that results from resistive loading of the crystal. The desired crystal oscillator should maintain proper amplifier biasing without degrading stable, low-noise operation at the resonant frequency. The oscillator should require no modification to operate at various frequencies, other than to change the crystal. Furthermore, the design of the oscillator should be such that it may be readily fabricated upon and within a common substrate, as an integrated circuit.
The problems outlined above may be addressed by a circuit and method disclosed herein for a crystal oscillator in which the operating point is biased without reducing the Q of the crystal. The circuit oscillates at a frequency defined by a resonant network containing the crystal and other reactive components. The present oscillator may employ an operational transconductance amplifier (OTA), containing bipolar or metal oxide semiconductor (MOS) transistors, to create a negative resistance. The negative resistance compensates for energy losses in the resistance within the resonant network, thereby sustaining oscillation. Other OTAs may be employed as gain and control elements within the oscillator circuit.
Conventional crystal oscillators maintain an operating point by means of bias resistors connected to the resonant network. The resistance of these bias resistors is typically lower than the effective parallel resistance of the crystal. Therefore, the bias resistors load the resonant network, reducing its Q. The Q directly influences the frequency stability and phase jitter of the oscillator, so lowering Q degrades the performance of the oscillator.
In contrast to the conventional approach, the oscillator circuit disclosed herein employs a feedback-controlled current source (i.e., the output of an OTA) to derive the operating point. The current source presents an extremely high impedance, and does not load the resonant network. This allows the resonant network to be operated at a higher Q, relative to conventional oscillator circuits, so oscillator performance is optimized. The OTA coupled to the resonant network employs a combination of positive feedback and negative feedback. Positive feedback is applied only at the desired frequency of oscillation, while negative feedback is applied at other frequencies to stabilize the oscillator.
A method for biasing a crystal oscillator without reducing the Q of the resonant network containing the crystal is also disclosed herein. The present method calls for using a controlled current source to bias the resonant network of the oscillator, instead of the bias resistors used in conventional crystal oscillators. The current source may be the output of an OTA, which appears as a high impedance to the resonant network, and does not degrade the Q through loading effects.
The method further describes the use of an oscillator amplifier as a negative resistance to enable continuous oscillation by compensating for resistive losses in the resonant network. The oscillator amplifier receives both positive and negative feedback. The positive feedback is applied only at the oscillation frequency, while the negative feedback is applied at other frequencies to stabilize the oscillator amplifier.